Chessboard Proof

Hey there I also need some help on this proof as well.

Imagine an infinite chessboard that contains a positive integer in each square. If the value in each square is equal to the average of its four neighbors to the north, east, south and west prove the values in all the squares are equal.

I understand this problem conceptually, but I can seem to put this in words. I hope someone can guide me through the problem step by step, so I can understand how to do this problem, thanks.

Re: Chessboard Proof

Re: Chessboard Proof

Hey thanks a lot for getting me started on this problem, just one question I'm not exactly sure what those symbols mean like phi and ZxZ. I am hoping you can let me know what they mean just so I can understand what each part means.